From quantum to elliptic algebras |
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Authors: | J Avan L Frappat M Rossi P Sorba |
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Institution: | (1) LPTHE, CNRS-URA 280, Universités Paris VI/VII, France;(2) Centre de Recherches Mathématiques, Université de Montréal, Canada;(3) Laboratoire de Physique Théorique ENSLAPP, Annecy-le-Vieux Cédex;(4) ENS Lyon, Lyon Cédex 07, France |
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Abstract: | It is shown that the elliptic algebra
at the critical level c = –2 has a multidimensional center containing some trace-like operators t(z). A family of Poisson structures indexed by a non-negative integer and containing the q-deformed Virasoro algebra is constructed on this center. We show also that t(z) close an exchange algebra when p
m = q
c+2 for
, they commute when in addition p = q
2k
for k integer non-zero, and they belong to the center of
when k is odd. The Poisson structures obtained for t(z) in these classical limits contain the q-deformed Virasoro algebra, characterizing the structures at p q
2k
as new
algebras. |
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Keywords: | |
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